Question: Simplify the following expression: $q = \dfrac{-10t^2 - 20t + 240}{t - 4} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-10$ , so we can rewrite the expression: $ q =\dfrac{-10(t^2 + 2t - 24)}{t - 4} $ Then we factor the remaining polynomial: $t^2 + {2}t {-24} $ ${-4} + {6} = {2}$ ${-4} \times {6} = {-24}$ $ (t {-4}) (t + {6}) $ This gives us a factored expression: $\dfrac{-10(t {-4}) (t + {6})}{t - 4}$ We can divide the numerator and denominator by $(t + 4)$ on condition that $t \neq 4$ Therefore $q = -10(t + 6); t \neq 4$